A052778 E.g.f.: x^4*log(-1/(-1+x)).

0, 0, 0, 0, 0, 120, 360, 1680, 10080, 72576, 604800, 5702400, 59875200, 691891200, 8717829120, 118879488000, 1743565824000, 27360571392000, 457312407552000, 8109673360588800, 152056375511040000, 3005349539512320000, 62444484876533760000, 1360632459941314560000

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..450
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 735.

Crossrefs

Cf. A052747, A052794, A052759.

Programs

Maple

spec := [S,{B=Cycle(Z),S=Prod(Z,Z,Z,Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

a[n_] := If[n < 5, 0, n!/(n - 4)]; Array[a, 20, 0] (* Amiram Eldar, Oct 07 2020 *)
With[{nn=30},CoefficientList[Series[x^4 Log[-1/(x-1)],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Jun 28 2021 *)

Formula

E.g.f.: x^4*log(-1/(-1+x)).

Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=120, (-n^2+3*n+4)*a(n) + (n-3)*a(n+1)}.

a(n) = n! / (n-4) (n > 4). - Olivier Gérard, Jun 13 2001

Sum_{n>=5} 1/a(n) = 49/6 - 3*e. - Amiram Eldar, Oct 07 2020

Sum_{n>=5} (-1)^(n+1)/a(n) = 5/e - 11/6. - Amiram Eldar, Aug 20 2022

Extensions

New name using e.g.f. from Vaclav Kotesovec, Oct 07 2020